Motion fields describing the ocean surface dynamics live in vectorial spaces of high dimension. Consequently, their estimation from satellite images requires huge computational resources. The issue of dimensionality reduction, that is the determination of representative low dimensional structures in these high dimensional spaces, is of major importance for any application that demands real-time or short-term results. Proper Order Decomposition allows to determine such sub-space of motion fields on which estimation may be assessed with reduced complexity. A reduced model is obtained by Galerkin projection of evolution equations on this subspace. Motion is estimated by assimilating the observed image sequence with the reduced model. The paper describes how to derive the reduced space from a database of ocean model's outputs and explains how to estimate surface circulation from satellite sequences. Results are given on images acquired on the Black Sea basin by NOAA-AVHRR sensors.

The paper describes an operational method of rainfall now-casting based on ground radar acquisitions with high space and time resolution. The nowcast horizon is between 30 minutes and 1 hour as required by prevention measures of flash floods. The characteristics of the input data justify the design of an image-based method that estimates wind fields from image acquisitions and forecasts the location and quantity of rain in the near future. The estimation phase relies on an iterative data assimilation of the radar acquisitions with an evolution model of motion and image fields, while the forecast is obtained by simulating these fields at the chosen horizon. The research is done in the context of a collaboration with the french company Numtech and the data are obtained with radars of the company Weather Measures.

This paper describes modeling and numerical computation of orthogonal bases, which are used to describe images and motion fields. Motion estimation from image data is then studied on subspaces spanned by these bases. A reduced model is obtained as the Galerkin projection on these subspaces of a physical model, based on Euler and optical flow equations. A data assimilation method is studied, which assimilates coefficients of image data in the reduced model in order to estimate motion coefficients. The approach is first quantified on synthetic data: it demonstrates the interest of model reduction as a compromise between results quality and computational cost. Results obtained on real data are then displayed so as to illustrate the method.

This paper has two coupled objectives: estimating motion and tracking a given object on an image sequence. It relies on a data assimilation approach, that solves evolution equations of motion, those of image brightness, and those of the distance map modeling the object's boundary. The two last express the optical flow constraint, which assumes that image brightness and distance map are advected by velocity. The method assimilates contour points by an innovative approach combining two criteria. First, the boundary of the object should match contour points at acquisition dates; second, the control of the distance between each pixel and the object's boundary allows to better motion estimation on the whole domain. The method is tested on synthetic data and satellite acquisitions.

The paper addresses the estimation of motion on an image sequence by data assimilation methods. The core of the study concerns the definition of the data term, or observation equation, that links images to the underlying motion field. In the image processing literature, the optical flow equation is usually chosen to characterize these links. It expresses the Lagrangian constancy of grey level values in time. However, this optical flow equation is obtained by linearization and is no more valid in case of large displacements. The paper discusses the improvement obtained with the original non-linear transport equation of the image brightness by the velocity field. A 4D-Var data assimilation method is applied that solves the evolution equation of motion and the observation equation in its non-linear and linear forms. The comparison of results obtained with both observation equations is quantified on synthetic data and discussed on oceanographic Sea Surface Temperature images.

This paper describes a sliding windows assimilation method, that allows estimating motion on long temporal image sequences, thanks to data assimilation techniques. The method splits the initial temporal window in sub-windows, on which reduced models are computed that allow to process images in quasi-real time. The method is quantified with twin experiments to demonstrate its potential for processing long-term satellite data. The main perspective is to replace the bases Ψξof the reduced models, which are obtained with a Principal Order Decomposition, by a fixed basis. In that case, even the first sub-window could be processed by a reduced model, in order to further reduce the computational requirements. Moreover, this fixed basis should be defined as satisfying optimality criteria, which translate properties on motion fields and image data. In that way, the method will be able to process long satellite sequences acquired over a full basin, as the Black Sea.

This paper presents a real-time and dense structure from motion approach, based on an efficient planar parallax motion decomposition, and also proposes several optimizations to improve the optical flow firstly computed. Later, it is estimated using our own GPU implementation of the well-known pyramidal algorithm of Lucas and Kanade. Then, each pair of points previously matched is evaluated according to the spatial continuity constraint provided by the Tensor Voting framework applied in the 4-D joint space of image coordinates and motions. Thus, assuming the ground locally planar, the homography corresponding to its image motion is robustly and quickly estimated using RANSAC on designated well-matched pairwise by the prior Tensor Voting process. Depth map is finally computed from the parallax motion decomposition. The initialization of successive runs is also addressed, providing noticeable enhancement, as well as the hardware integration using the CUDA technology.

The paper presents a motion estimation method based on data assimilation in a dynamic model, named Image Model, expressing the physical evolution of a quantity observed on the images. The application concerns the retrieval of apparent surface velocity from a sequence of satellite data, acquired over the ocean. The Image Model includes a shallow-water approximation for the dynamics of the velocity field (the evolution of the two components of motion are linked by the water layer thickness) and a transport equation for the image field. For retrieving the surface velocity, a sequence of Sea Surface Temperature (SST) acquisitions is assimilated in the Image Model with a 4D-Var method. This is based on the minimization of a cost function including the discrepancy between model outputs and SST data and a regularization term. Several types of regularization norms have been studied. Results are discussed to analyze the impact of the different components of the assimilation system.

Indigenous lands represent an efficient way to protect indigenous communities and environment in Brazil. However, these lands are also highly affected y the land use changes occuring in its surroundings. We quantified the land use changes in the Xingu basin based on MODIS EVI data between 2000 and 2006. We estimated the deforested area inside and outside the indigenous lands, the crop expansion and intensification around the protected areas. Our results indicate that, even if indigenous lands are efficient to limit deforestation (97.5% of deforestation is outside the indigenous lands), crop expansion and intensification (double crop systems) are increasing rapidly, what may imply pollution of headwaters of the Xingu river which crosses the protected area.

The objective of this study is to compute the surface circulation velocity from oceanographic image sequences. Data assimilation provides a mathematical solution to combine optimally observations and models. We define a dedicatedImageModelconsistent with the physical knowledge of ocean dynamics. Satellite images are then assimilated into this model using a variational data assimilation scheme. This technique relies on the adjoint model definition to compute the minimum of a cost function measuring the discrepancy between model's outputs and observations. The method takes into account the physical knowledge of the ocean circulation, which is relevant for explaining images evolution and, in case of missing data due to clouds occlusion or lack of acquisitions, the estimation is still consistent with the physical evolution laws.

Apparent motion estimated on satellite data is used for example to compute the wind field in meteorology, and surface currents in oceanography. The satellite images display turbulent fluids with strong rotational patterns at different spatial and temporal scales. This specificity necessitates devising adapted methods, allowing to control the divergence and curl of the retrieved motion field. Vector spline methods are very adapted to that purpose. The vector spline problem is defined as finding a motion field that satisfies a temporal conservation equation at selected control points and that minimizes a regularity constraint in all the image domain. An exact solution of this problem can be found for the 2nd order div-curl regularity constraint. The retrieval of the solution does not require an iterative minimization procedure: a dense matrix must be inverted to compute the spline's coefficients. This matrix unfortunately becomes large and ill-conditioned as the number of control points increases, making the vector spline approach unsuitable for processing large satellite images. This paper presents a method called "Partition of Unity and Optical Flow" (PUOF), based on a decomposition of the spatial domain: local vector splines are computed in subdo-mains of the image, then merged using a partition of unity algorithm. The resulting motion field is a good approximation of the exact vector spline solution, and its retrieval is numerically stable and computationally affordable even when processing large data sets, as demonstrated by results obtained on sequences of synthetic and meteorological images.

In this study, we show how different spectral channels of NOAA-AVHRR acquired data can be used to produce a synthetized signal aimed at helping the characterization of plumes associated to fire events. The synthetized signal is computed using a reconstruction formula in the multifractal microcanonical formalism (herein referred to as MMF). The MMF is a recent development in the analysis of complex signals, well adapted to the study of turbulent acquired data, for instance geophysical fluids. It allows the computation, at each point of the signal's domain, of a singularity exponent, characteristic of the scale behaviour of the signal around that point; singularity exponents provide information about the strengths of the transitions inside a signal, and they are related to the multifractal hierarchy associated to structure functions in Fully Developped Turbulence (FDT). In the MMF, it is possible to reconstruct a turbulent signal from the manifold of most singular exponents. We make use of this property by computing supergeometric structures from a thermal infrared channel in NOAA-AVHRR acquired data, and we use the signal's gradient coming from other channels to reconstruct a signal in which plume pixels are easier to detect. This methodology is based on the turbulent properties of the plume accessible from the thermal infrared band; the algorithm is detailed and applied on a specific example, showing a new spatially-based method for helping the determination of plume pixels in NOAA-AVHRR data.

We tackle the problem of coupling a geophysical simulation model with data coming from image processing. It needs to define the image observation space and to design an operator to transform results from the image space to the model space. In this study, we use a shallow-water oceanographic circulation model developed at MHI. We propose a processing chain first based on an image processing step relying on a dedicated motion estimation operator, and then a data assimilation step of the estimated velocity. We illustrate the method on different results without and with assimilation

This paper aims at estimating the apparent velocity from sequences of satellite images. This study is an illustration of a more general methodology for generating, from satellite images, pseudo-observations of physical variables, that are assimilated within a geophysical forecast model in view of improving the quality of its results. In the case of the presented study, the used satellite images are sequences of sea surface temperature (SST), from which pseudo-observations of sea surface velocities are generated, and assimilated within an ocean circulation model. The originality of the approach lies in the definition of an image model, that predicts the evolution of image information -here, SST- as a function of the pseudo-observations -here, surface velocity-. Satellite data are then assimilated within the image model, yielding an estimation of the pseudo-observations. In the case of this paper, this methods allows the estimation of sea surface velocities, even when large parts of the satellite images are corrupted by clouds. The image model plays the role of an intermediate model, between satellite data and the forecast model, and allows the assimilation of image information which is not directly linked to the state variables of the forecast model.

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We are interested in the problem of modeling the propagation of landslides. We use an image processing approach based on the computation of a geodesic distance map. We determine the evolution of an initial curve along a given surface. The model can incorporate various properties coming from the geometry of the surface or independant measures. In an application, we focus on landslides study in the context of natural risk management The model is driven by geometrical constraints and SAR interferometric measures.

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In this paper, we propose a scheme for a land cover classification process from satellite images, with inclusion of topographic effects (elevation) available from a digital elevation model. First, we study and analyse errors provided from the relief on an available non-topographic classification image. We then present a classification process which takes into account, for each land cover type, the non-unicity of reflectance values according to the elevation. We build a new "topographic classification", whose results and their analysis are presented.

This paper concerns the characterization of clouds on meteorological satellite image sequences through points trajectories. These temporal curves can be computed from the result of motion estimation over image sequences. The study includes a representation method for the trajectories, which is based on normalized Fourier modules. The original trajectories can be compared independently of their localization, orientation and scale. We then determine that the information contained in these representation vectors is relevant for discrimination and classification of cloudy structures on satellite data. Results addressing METEOSAT infrared data are analyzed and displayed throughout the paper.

This paper addresses the issue of motion estimation on image sequences. The standard motion equation used to complete the apparent motion of image irradiance patterns is an invariance brightness based hypothesis called the optical flow constraint. Other equations can be used, in particular the extended optical flow constraint, which is a variant of the optical flow constraint, inspired by the fluid mechanic mass conservation principle. In this paper we propose a physical interpretation of this extended optical flow equation and a new model unifying the optical flow and the extended optical flow constraints. We present results obtained for synthetic and meteorological images.

The general problem of surface matching is considered in this study. The process described in this work hinges on a geodesic distance equation for a family of surfaces embedded in the graph of a cost function. The cost function represents the geometrical matching criterion between the two 3D surfaces. This graph is a hypersurface in 4-dimensional space, and the theory presented herein is a generalization of the geodesic curve evolution method introduced by R. Kimmel et al. (1995). It also generalizes the 2D matching process developed in Cohen and Herlin (1998). An Eulerian level-set formulation of the geodesic surface evolution is also used, leading to a numerical scheme for solving partial differential equations originating from hyperbolic conservation laws, which has proven to be very robust and stable. The method is applied on examples showing both small and large deformations, and arbitrary topological changes.

We investigate an original method to compute the optical flow on image sequences. Instead of assuming invariance principles applied to individual pixels, this method considers objects as a whole, by constraining their total intensity during their motion. A variational implementation of this method has already been studied. We propose here a parametric implementation of this method using an affine prior model. A combined method between the variational method and the affine method is proposed in order to capture both affine components and non-affine components. Results on meteorological infrared data are presented.

Tackles the general problem of surface tracking. The authors present a new method based on the computation of geodesic distance maps between a source and a destination surface. The method used in this case is a generalization to the case of surfaces of a 2D matching process introduced by Cohen and Herlin (1998). It relies on a level-set formulation, thus providing stable and robust resolution schemes. The obtained matching method accommodates both small and large deformations. Actually, the matching constraints are explicitly expressed by the definition of a hypersurface. The connecting paths between the two surfaces lie on this hypersurface. The authors construct a hypersurface that allows the matching process to preserve geometric similarities in the case of small deformations, and loosen these geometric constraints when large deformations occur. The applicative framework is the study of the Earth's crustal evolution to characterize the deformation of digital elevation models.

In this study the problem of modeling a family of curves is addressed. The need of such modeling appears frequently in many aspects of image processing where many linear structures keep spatial relationships during their evolution. We present a modeling tool well suited to the spatial modeling of a family of curves, and which can be very useful for motion tracking and curve evolution as well. The family of curves is represented as the line paths (orbits) of a "spline vector field", i.e. a vector field interpolating data using a framework similar to the theory of spline curves. The model is exemplified with oceanic satellite data. Its usefulness for curve evolution modeling is also presented.

Motion estimation is one of the main subjects in computer vision. Many methods developed to compute motion make use of the optical flow hypothesis. These methods usually fail to capture motion of objects with intensity evolution. We propose a new approach to solve the motion computation problem with a different type of constancy hypothesis. Because we are mainly interested in deformable moving structures, we postulate that such a structure, within a temporal image sequence, is associated with a constant volume or a constant total intensity over time. We call this postulate the volume conservation hypothesis. Results are displayed for clouds motion and deformation on meteorological satellites images.

We present a method for matching curves which accommodates large and small deformation. The method preserves geometric similarities in the case of small deformation, and loosens these geometric constraints when large deformations occur. The approach is based on the computation of a set of geodesic paths connecting the curves. These two curves are defined as a source area and a destination area which can have an arbitrary number of connected components and different topologies. The applicative framework of the presented method is the study of the crustal deformation from a set of iso-elevation curves. An experiment with real curves demonstrates that the approach can be successfully applied to characterize deformation of Digital Elevation Models.

This paper addresses vegetation monitoring in European agricultural areas using Earth Observation satellites. Due to the small size of typical European fields, two complementary sensors are used, SPOT and NOAA-AVHRR, bringing the spatial and the temporal information respectively. A sub-pixel analysis of NOAA data using one SPOT image is performed to characterize fields with high spatial and temporal resolutions. To be used in an operational context, the method must have realistic data requirements. We define an operational scenario making use of only one SPOT image per site and a one year NOAA sequence, covering a large part of Europe. We first proceed to an unsupervised segmentation of the SPOT image; the NOAA data analysis on test sites provides the temporal evolution of vegetation; then, identification of fields is performed by minimizing a cost function measuring the similarity between the global reflectance observed on NOAA pixels and the reflectance computed from corresponding regions at SPOT resolution.

Repeat-pass SAR interferometric data are multitemporal and display changes occurring between two acquisitions. As a consequence, phase and correlation images contains meaningful information that are usable for cropland monitoring. This paper proposes a statistical model to segment high phasimetric structures. It is expressed in a Markov random field framework by using cooperatively phase and correlation information.

This paper is concerned with the problem of tracking clouds structures like vortices in meteorological images. For this purpose we characterize the deformation between two successive occurrences, by matching their two boundary curves. Our approach is based on the computation of the set of paths connecting the two curves to be matched. It minimizes a cost function which measures the local similarity of the two curves. These matching paths are obtained as geodesic curves on this cost surface. Moreover our method allows to consider complex curves of arbitrary topology since these curves are represented through an implicit function rather than through a parameterization. Experimental results are given to illustrate the properties of the method in processing synthetic and then meteorologic remotely-sensed data.

Important SAR phasimetric effects can be observed on the evolution of vegetation subjected to rainy periods. We present a segmentation model to detect these artefacts. It is based on a statistical model, expressed in a Markovian random field framework. The novelty of the approach resides in the use of both interferometric phase and coherence.

Describes a fusion process between two different data sources, one providing an accurate spatial information, the other providing time series with a much coarser spatial scale. It is applied in the following remote sensing context: the forecast of cereals production, which is a challenging application of the new generation of Earth observation satellites. These two data types are required since agronomical models must be fed with a daily sampling of cereals reflectances, and since in Europe, fields have a relatively small size. SPOT-XS is wed to provide spatial information at the parcels level, a meso-scale sensor (here, NOAA-AVHRR), which outputs images of large areas every day, provides the temporal information. The combination of these two data sources makes it possible to daily estimate reflectances of main cultivations at the parcels level. The selected approach is as follows: a preliminary learning stage provides the reflectances of each type of cultivation; then operational scenarios are defined to apply the learning information in order to estimate statistics on large areas: using only one SPOT-XS image and meso-scale daily images, a fusion scheme makes it possible to obtain land use identification at high spatial resolution with its temporal behavior.

Presents a segmentation method to detect effects due to high temporal evolution of the interferometric phase. The segmentation of these phasimetric artefacts is performed, taking into consideration both phase image and interferometric correlation. The process is based on a statistical model, robust in a noisy environment. It is expressed in a Markovian random field framework. This work is particularly original in respect to its application domain. The major novelty of the approach resides on the use of two pieces of information in order to correspond exactly to the effects definition. It is used to segment phasimetric effects, appearing on some kind of ground occupation, due to rainy events.

To analyze SAR interferometric data, an unwrapping process must be first performed. Most so far proposed solutions use either local or global methods. In this paper we propose a mixed method to solve this problem, based on a 3-step iterative process: a local unwrapping is first performed and then improved through a Markovian segmentation, false unwrapped residues are finally detected and corrected. A deterministic algorithm is used for the relaxation process; wrong unwrapped areas are corrected by a backtracking mechanism. Some results obtained by this approach, which presents a lower computational cost compared to complex stochastic unwrapping methods, are also presented.

Motion study in computer vision highly depends on the type of imagery and on the kind of the studied objects. A popular approach of non-rigid motion supposes that the objects are continuously and locally deformed. Local features, such as curvature extrema, are then often used. However, these features can not always be accurately computed, and motion may involve large deformation of the object between two consecutive temporal occurrences. In these cases, a real need exists for an approach that does not rely on local features. That study of motion requires additional information. We introduce a geometrical evolution model that enables one to generate a surface interpolating successive contours of the object during its temporal evolution. This geometrical model may be viewed as a simplification of a true physical model of motion. This approach is particularly well suited to remote sensed data: structures of interest do not have a well defined shape, and the temporal resolution may be poor, involving large deformation. The model is successfully applied to vortex tracking on sea color and meteorologic images.

This paper studies the problem of face identification for the particular application of an automatic cash machine withdrawal: the problem is to decide if a person identifying himself by a secret code is the same person registered in the database. The identification process consists of three main stages. The localization of salient features is obtained by using morphological operators and spatio-temporal information. The location of these features are used to achieve a normalization of the face image with regard to the corresponding face in the database. Facial features, such as eyes, mouth and nose, are extracted by an active contour model which is able to incorporate information about the global shape of each object. Finally, the identification is achieved by face warping including a deformation measure.

This work is devoted to segmentation and tracking of structures undergoing large deformation in an image sequence. The overall goal is the modeling of complex moving and deforming structures that simultaneously brings compression of data, segmentation and tracking on temporal sequences of images. Deforming entities are approximated by implicit templates, defined as level sets of some particular implicit functions. Implicit functions provide interesting tools for the modeling of visco-elastic objects. Structures are approximated using an energy minimization process; the energy functional carries information about position, tangent and curvature. The implicit functions are defined by some control points, their radius of influence, and an iso-value. Once the structures are segmented, tracking is modeled using the displacements of the control points and the variation of the radii of influence. The method is first applied on a sequence of images displaying a vortex formation, and the authors show that such a vortex structure can be segmented and tracked with implicit functions.

This paper is concerned with three main problems of image processing occuring on temporal sequences of satellite oceanographic images: approximate localization of the interesting structures on the images; segmentation or determination of the boundary of the structures; and temporal tracking of these boundaries to illustrate their evolution. In this paper, application is done on vortices and results are displayed all over the paper. For this purpose, we propose a new method for optical flow computation and interpretation and a geometric modelling of the structures. Oceanographic images obtained from environmental satellite platforms present a new challenge in computer science. The huge amount of data collected each day and the need for characterizing some specific structures on these images for oceanographic monitoring justify our approach for the detection and tracking of vortices on oceanographic images.

Spatiotemporal segmentation in echocardiographic image sequences is discussed. Spatial properties and temporal properties are combined to compute segmentation and tracking in a single process. The Markov random field (MRF) framework is used for modeling the energy function. Starting from a reference image, where a manual segmentation is made, a method is developed to estimate the model parameters. An estimation is a crucial point in MRF models. Thus, given an initial segmentation of the sequence, this approach can segment and track a cardiac cavity during the cardiac cycle. Its performance is demonstrated on a real echocardiographic sequence.>

The problem of improving an initial segmentation of medical data by making use of gray level, texture, and gradient information is addressed. The mathematical environment is that of Markov random fields and stochastic processes. This yields two major advantages: automatic selection of program parameters and ergonomic software that can be used to test homogeneity properties of regions. The method is applied to echocardiographic images in order to segment cardiac cavities.>

Presents a Markov random field model designed to construct a segmentation of echocardiographic images from an initial segmentation. An iterative procedure for estimating the model parameters is described and results are presented for a sequence of cardiac images in order to segment cardiac cavities.>

A hierarchical set of operators for texture analysis is presented. The method used is to code the local frequency resonance of these operators but not their simple responses. Therefore, the texture features obtained are stable. The operators fulfil the conditions described by J.P. Crettez (1984) in his work on the visual system model. The procedure is used to automatically determine the resolution of homogeneous texture, the resolution being the minimum window size capable of giving stationary features. All the samples of suitable size then have the same signature coding the local feature of texture.>